Fuel cell bipolar plates with flow uniformity

ABSTRACT

A bipolar plate with an enhanced fluid flow field design is provided for improved flow uniformity. The bipolar plate includes an inlet, an outlet, and a flow field having a pattern defining a plurality of microchannels configured to provide fluid communication between the inlet and the outlet. The pattern includes a plurality of channels with discrete areas of discontinuity to direct fluid from the inlet to the outlet. The pattern is designed using an inverse permeability field and is based on a reaction-diffusion algorithm to model channel spacing, thereby providing a variable pitch microchannel pattern. In various aspects, Gray-Scott reaction-diffusion equations may be used to obtain an anisotropic microchannel layout. Methods may include optimizing a porous media model domain for one of: a minimum flow resistance across the domain, a uniform velocity across a direction of the domain, and a minimum velocity across a direction of the domain.

TECHNICAL FIELD

The present disclosure generally relates to fuel cell bipolar platesand, more particularly, to designs for tailoring and customizing theflow fields of bipolar plates to control a fluid flow pattern and flowuniformity.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it may be described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presenttechnology.

Bipolar plates useful with fuel cell technology are designed to permitthe transfer of air or fuel from an inlet, through a flow field, and toan outlet. The flow fields of the bipolar plates may include channelscommonly formed by machining or stamping techniques. The efficiency ofthe chemical reaction within the fuel cell is based, in part, on theproper flow and distribution of air and fuel fluid flow streams. Thefluid distribution is, in turn, based on the channel network and design.A uniform fluid flow is important to both performance and cost. Variousdesigns of flow fields for bipolar plates often include portions withstraight channels, and portions with channel designs that are manuallyoptimized by using computational fluid dynamics in order to determinewhich portions of a flow field should be solid, and which portionsshould be provided for the fluid transfer. The manual optimization isboth time consuming and costly.

Accordingly, it would be desirable to provide improved, cost effectivebipolar plate designs and methods of manufacture that include anoptimized fluid flow field distribution that can be customized.

SUMMARY

This section provides a general summary of the disclosure and is not acomprehensive disclosure of its full scope or all of its features.

In various aspects, the present teachings provide a method for designinga microchannel layout for a flow field of a bipolar plate. The methodmay include defining a fluid flow optimization domain with boundaryconditions and loads. The fluid flow optimization domain has an x-axisdefining a longitudinal direction from an inlet leading to an outletwindow of the flow field, a y-axis defining a transverse direction, anda z-axis perpendicular to the x-axis and the y-axis. The method mayinclude using a gradient-based algorithm together with computationalfluid dynamics to optimize a porous media model domain. This may includesetting a minimum inverse permeability to a non-zero value and obtaininga grayscale design and fluid velocity field. The method may then useGray-Scott reaction diffusion equations with the grayscale design andfluid velocity field in order to obtain a microchannel layout with aplurality of channels. The method includes providing the plurality ofchannels with discrete areas of discontinuity and incorporating themicrochannel layout as a pattern for an inlet region of the flow fieldof the bipolar plate. In various aspects, the discrete areas ofdiscontinuity are disposed along spaced apart contour lines based on apredetermined performance parameter of the bipolar plate

In other aspects, the present teachings provide a method for designingan anisotropic microchannel layout for a flow field of a bipolar plate.The method may include defining a fluid flow optimization domain withboundary conditions and loads. The method may include using agradient-based algorithm together with computational fluid dynamics tooptimize a porous media model domain. This may include setting a minimuminverse permeability to a non-zero value and obtaining a grayscaledesign and fluid velocity field. The method may then use the Gray-Scottreaction diffusion equations and an anisotropic diffusion tensor alongwith the grayscale design and fluid velocity field and to generate ananisotropic microchannel layout having a connected line and spacepattern including a plurality of channels. The plurality of channels areprovided with discrete areas of discontinuity. The anisotropicmicrochannel layout is incorporated as a pattern for an inlet region ofthe flow field of the bipolar plate to provide flow uniformity.

In still other aspects, the present teachings provide a bipolar platefor a fuel cell including an inlet, an outlet, and a flow field. Theflow field includes an inlet region having a pattern defining aplurality of anisotropic microchannels configured to provide fluidcommunication between the inlet and the outlet. The anisotropicmicrochannels are defined having discrete areas of discontinuity. Thepattern of the flow field is designed using an inverse permeabilityfield and solving Gray-Scott reaction-diffusion equations with ananisotropic diffusion tensor to obtain an anisotropic microchannellayout with channel spacing based on effective medium theory. In variousaspects, the discrete areas of discontinuity are disposed along spacedapart contour lines based on a predetermined performance parameter ofthe bipolar plate selected from at least one of pressure flow andvelocity flow.

Further areas of applicability and various methods of enhancing theabove technology will become apparent from the description providedherein. The description and specific examples in this summary areintended for purposes of illustration only and are not intended to limitthe scope of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawings will be provided by the Office upon request and paymentof the necessary fee.

The present teachings will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 illustrates a schematic plan view of an exemplary bipolar plateassembly for a fuel cell useful according to various aspects of thepresent technology;

FIG. 2 is a magnified view of a portion of the bipolar plate assembly ofFIG. 1 represented by the shape labeled with reference number 2;

FIG. 3 is an alternate view of the portion of the bipolar plate assemblyof FIG. 2 provided with a simplified inlet design and illustrating amagnified portion of a flow field outlet window region;

FIG. 4 illustrates an exemplary schematic flow chart for designing apattern for an inlet region of a flow field;

FIG. 5 is a flowchart of an exemplary gradient based algorithm usingmethod of moving asymptotes (MMA) or globally convergent method ofmoving asymptotes (GCMMA) looped in with the fluid flow CFD to optimizethe domain;

FIG. 6 provides a schematic illustration a fictitious design variable ofdensity γ that may be introduced to relax the topology optimizationproblem and provide a numerical framework to establish flowoptimization;

FIG. 7 provides an illustration of a flow field with the inversepermeability κ_(min) being equal to zero, and represents a strictlyblack & white (0, solid and 1, fluid) design;

FIG. 8 provides an illustration of an exemplary grayscale designrepresenting a porous medium with the inverse permeability κ_(min) beingequal to one third of the maximum, for example, κ_(min)=0.333 κ_(max);

FIG. 9 illustrates an exemplary method flow chart for designing apattern for an inlet region of a flow field using an anisotropicdiffusion tensor;

FIG. 10 illustrates an exemplary schematic generally summarizing themethods for designing a pattern for an inlet region of a flow field;

FIG. 11 illustrates an exemplary pressure field obtained from anoptimized porous media inlet flow field model;

FIG. 12 illustrates a line graph of a velocity profile associated withthe pressure field of the optimized porous media inlet flow field modelof FIG. 11;

FIG. 13 illustrates a resulting pressure field obtained from acontinuous channel design of the optimized porous media inlet flow fieldmodel of FIG. 11;

FIG. 14 illustrates a line graph of a velocity profile associated withthe pressure field of the continuous channel inlet flow field design ofFIG. 13;

FIG. 15 illustrates a resulting pressure field obtained from adiscontinuous channel design of the optimized porous media inlet flowfield model of FIG. 11 having a substantially uniform inlet feed rate;

FIG. 16 illustrates an exemplary design of a flow field with adiscontinuous channel inlet flow field design according to anotheraspect of the present technology and having a non-uniform inlet feedrate;

FIG. 17 illustrates an exemplary velocity field obtained from anoptimized porous media inlet flow field model;

FIG. 18 illustrates a resulting velocity field obtained from adiscontinuous channel design model of the optimized porous media inletflow field model of FIG. 17;

FIG. 19 is a graph that shows the results of a comparison between adiscontinuous channel inlet velocity field and a target specificationvelocity field; and

FIG. 20 illustrates a cross-sectional view of an exemplary set ofchannels and walls that can be made according to various manufacturingtechniques.

It should be noted that the figures set forth herein are intended toexemplify the general characteristics of the methods, algorithms, anddevices among those of the present technology, for the purpose of thedescription of certain aspects. These figures may not precisely reflectthe characteristics of any given aspect and are not necessarily intendedto define or limit specific embodiments within the scope of thistechnology. Further, certain aspects may incorporate features from acombination of figures.

DETAILED DESCRIPTION

The present technology generally teaches an optimized bipolar platestructure and/or assembly for a fuel cell, along with methods of designand manufacturing. The bipolar plates used in the structure and/orassembly can be provided with a flow field that can be designed with aplurality of channels, also referred to as microchannels, to provide thebipolar plate with a tailored and customized design. The channels of thepresent technology are defined having discrete areas of discontinuitythat provide an increased uniformity in fluid flow. The pattern of theflow field may be designed using an inverse permeability field andsolving Gray-Scott reaction-diffusion equations with an anisotropicdiffusion tensor to obtain an anisotropic microchannel layout withchannel spacing based on effective medium theory. In various aspects, atleast a portion of the discrete areas of discontinuity are disposedalong spaced apart contour lines that may be based on a predeterminedperformance parameter of the bipolar plate. For example, thepredetermined performance parameter may be at least one of pressure flowand velocity flow.

In various aspects, methods for designing a microchannel layout for aflow field of a bipolar plate include defining a fluid flow optimizationdomain with boundary conditions and loads. The methods may includeperforming an interpolation process to design a flow distributionnetwork. Using a gradient-based topology optimization algorithm, loopedin together with fluid flow computational fluid dynamics, the domain isthen optimized for minimum flow resistance (with optional mass flow rateconstraints at fluid outlet boundaries) using a modified Darcy flowequation for porous media. In other aspects, the domain optimization canbe based on obtaining a uniform velocity across a direction of thedomain, or a minimum velocity across a direction of the domain. Incontrast to various topology optimization techniques, a non 0-1(solid-fluid) design is obtained with grayscale throughout the domain.For example, a material interpolation approach is used where the methodincludes setting the minimum inverse permeability to a non-zero value(with the maximum permeability representing a porous medium), andobtaining a grayscale design and fluid velocity field. Using Gray-Scottreaction diffusion equations with the grayscale design and fluidvelocity field, the method includes obtaining a microchannel layout. Thechannel spacing can be based on effective medium theory for flow throughporous media. In various aspects, the permeability of the optimizeddesign space is linked to the microchannel design layout through ananisotropic definition of the diffusion coefficients of the Gray-Scottreaction diffusion equations in order to obtain an anisotropicmicrochannel layout. The use of present technology eliminates theexplicit modeling of the microchannels. Instead, it derives a channeldesign using a computationally efficient post-processing technique basedon the Gray-Scott equations and the velocity flow field through theporous medium. The discontinuous channel design is able to recover theporous model pressure field distribution with a high degree of accuracy,and also provides a match between models for an optimized velocityfield. For example, in various aspects, the discontinuous channel designis able to meet target velocity flow rate specifications with less thanabout 5% of an average outlet flow rate variation.

The optimized design for the microchannel layout is then incorporated asa pattern for the flow field of the bipolar plate. For example,fabrication techniques can be used, in combination with the pattern, tocreate a network of functionally graded microchannels, a porous media,or a hybrid combination thereof. As will be described in more detailbelow, additive manufacturing techniques can be used where the flowfield, or portion thereof, is fabricated using laser sintering, e-beammelting, and/or binder jet technology that may use a combination ofprinting and curing. Electroplating techniques may also be used forfabricating a functionally graded porous medium. A commerciallyavailable permeable material or functionally graded porous medium can beused. In other aspects, the porous medium can be custom made. In someexamples, metal inverse opal technology can be used with a suitablemetal, such as copper, nickel, or titanium. The functionally gradedporous medium is generally obtained by templating polystyrene particlesof different sizes, and/or controlling a sintering time for differenttemplated regions. Conventional metal machining and/or stampingtechniques can be used in combination with the above techniques toultimately provide the bipolar plates.

FIG. 1 illustrates a schematic plan view of an exemplary bipolar plateassembly 20 that may be used with a fuel cell (not shown), such as a PEMfuel cell, according to various aspects of the present technology.Bipolar plate assemblies 20 are important components of PEM fuel cells,and have commonly been made of graphite or metals, such as stainlesssteel, aluminum, and titanium; composite bipolar plates have also beenused. Bipolar plate assemblies 20 typically supply fuel and oxidant toreactive sites adjacent the membrane, remove reaction products, collectcurrent produced by the internal reaction, and provide the necessarymechanical support for a plurality of fuel cells in a fuel cell stack.

By way of background, bipolar plate assemblies may include an anode flowfield plate and a cathode flow field plate that have been bonded orotherwise appropriately sealed together as an assembly. In certaininstances, they may be bonded to form a sealed coolant flow fieldbetween the plates, as commonly employed in the art. Various transitionchannels, ports, ducts, and other features involving all three operatingfluids (i.e. fuel, oxidant, and coolant) may also appear on the inactiveside and other inactive areas of bipolar plate assemblies. The operatingfluids may be provided under significant pressure, thus it is importantthat all of the features in the plates are appropriately sealed toprevent leaks between the fluids and to the external environment.Another feature for bipolar plate assemblies is that there is asatisfactory electrical connection between the two plates because asubstantial current generated by the fuel cell stack must be able topass between the two plates.

The plates making up the assembly may optionally be metallic and aretypically produced by stamping the desired features into sheets ofappropriate metal materials (e.g. certain corrosion resistant stainlesssteels). Two or more stamped sheets are then typically welded or clampedtogether with gaskets so as to appropriately seal all the fluid passagesfrom each other and from the external environment. Additional welds maybe provided to enhance the ability of the assembly to carry electricalcurrent, particularly opposite the active areas of the plates. Metallicplates may however be bonded and sealed together using adhesives or theaforementioned gaskets. Corrosion resistant coatings are also oftenapplied before or after assembly.

In other aspects, the present technology provides monolithic and/orhybrid structure bipolar plate assemblies. As used herein, the term“monolithic” means a single, unitary component that is intractablyindivisible once formed. While there may be an interface region wheretwo or more components are joined together by bonding or some type offusion, once the materials are bonded/fused to one another, thematerials do not typically separate from one another as may occur inother layered substrates. The bipolar plates may include porousmaterials and functionally graded materials as a base structure, and/ormay include portions that include a material created by additivemanufacturing techniques, electroplating techniques, and the like. Asused herein, the term “hybrid” structure means a structure that includesmore than one type of material or structure, for example, onenon-limiting aspect may include a first portion including a porousmedium, and a second portion with explicit microchannels, which may becreated by additive manufacturing techniques, electroplating techniques,and the like. In other non-limiting aspects, a hybrid porous structuredmaterial may include a first portion/region that is non-porous, and asecond portion/region that is porous with a certain permeability. Thedesign and manufacturing of monolithic and hybrid structure types ofbipolar plates and/or bipolar plate assemblies made with additivemanufacturing techniques and electroplating techniques will be describedin more detail below.

With renewed reference to FIG. 1, the structure of the bipolar plateassembly 20 generally includes at least one basic support substrate orbipolar plate structure 22 defining one or more inlet 24 and outlet 26,and a flow field 28 that cooperates with the bipolar plate 20 providingfluid communication between a respective inlet 24 and outlet 26. Theflow field 28 may be provided with one or more different regions havinga respective shape or pattern that defines a plurality of channels 30,or microchannels, sized and configured to provide the appropriate fluidcommunication. While one or more of the regions may be provided withgenerally straight, parallel, and/or serpentine style flow channels, invarious aspects, certain of the channels and/or portions of the flowfield, such as the inlet region 32 and/or outlet region 34, may beshaped and oriented in order to specifically minimize flow resistanceand to provide a minimal fluid power/pressure drop or to provide auniform flow field across the plurality of microchannels. In addition toproviding fluid communication between an inlet 24 and a respectiveoutlet 26, the channels 30 may serve as a support structure for othercomponents and the membrane and provide fluid transfer of the fuel andair to a respective anode diffusion layer and a cathode diffusion layer,which are then directed to the catalyst layers and reaction sites. Aswill be described in more detail below, various channels or portionsthereof may be provided with discrete areas of discontinuity in thechannel walls. This may provide for “branching” of the channels, whichmay operate similar to a manifold, allowing fluid flow through differentbranches, into and through several different openings.

FIG. 2 is a magnified view of a portion of the bipolar plate assembly 20of FIG. 1 represented by the shape labeled with reference number 2. Theportion shown in FIG. 2 includes an inlet 24 and the inlet region 32 ofthe flow field 28. As shown in FIG. 3, for ease of design, modeling, andexplanation herein, the inlet 24 is simplified as having a circularshape that is then used for obtaining the domain and data foroptimization described herein. The present technology generally focuseson the design of a flow pattern and microchannel designs of the inletregion 32 of the flow field 28, as shown in FIG. 2, so that it can bedesigned and configured with a plurality of microchannels and discreteareas of discontinuity to provide the inlet region 32 of the bipolarplate with a tailored and customized porosity and permeability thatincludes an improved flow uniformity. In broad terms, porosity isgenerally a measure of how much of a substrate is open space. This openspace can be, for example, between grains or within cracks, cavities,and/or channels provided within or on a surface of the substrate.Permeability is generally a measure of the ease with which a fluid canmove through the porous substrate.

FIG. 4 provides an exemplary schematic flow chart for designing apattern for an inlet region of a flow field. The method may begin withcalculating minimum and maximum permeability values from designconstraints in order to obtain an effective permeability of a channelarray. The fluid flow optimization domain, boundary conditions, andloads may be defined. Minimum and maximum values to bound thepermeability field value may be used to execute topology optimization.As is known in the art, topology optimization is a mathematical methodthat optimizes a material layout within a specific design space, basedon a particular set of loads, boundary conditions, and constraints, inorder to maximize the performance of the specific system. In variousaspects, a gradient-based algorithm, together with computational fluiddynamics (CFD), may be used to optimize the domain for minimum flowresistance. FIG. 5 is a flowchart of an exemplary gradient-basedalgorithm using method of moving asymptotes (MMA) or globally convergentmethod of moving asymptotes (GCMMA) looped in with the fluid flow CFD tooptimize the domain. In this instance, the optimization determines wherein a flow field design domain to place the channels and where to placethe fluid. In various aspects, results obtained from certain topologyoptimizations can be directly manufactured using various additivemanufacturing techniques. For the topology optimization, one generalapproach is to represent a structural configuration by a materialpresence at each point. As such, the present technology provides aflexible method for design of fluid flow manifolds under laminar flowconsiderations. With reference to FIG. 6, a fictitious design variableof density γ may be introduced to relax the problem and provide anumerical framework to establish flow optimization. FIG. 6 shows thevarious possibilities, with γ=1 representing a fluid state (essentiallywhite in FIG. 6), γ=0 representing a solid or low-permeability solid, orsolid (essentially black in FIG. 6). The grayscale coloring in FIG. 6represents an intermediate state with 0<γ<1, somewhere between a fluidstate and a solid state. Topology optimization is then applied to thesolid-fluid manifold design problem.

Based on the incompressibility condition of ∇·u=0, where u is the fluidvelocity, one can arrive at the Navier-Stokes equation for flow througha porous medium, as follows:

ρ(u·∇u)=−∇P+∇{η[∇u+(∇u)^(T)]}−κ_(e)(γ)u

where κ_(e) represents the effective inverse permeability. As anon-limiting example, the effective inverse permeability (convex)interpolation may then be provided as follows, with permeability as afunction of γ, the design variable:

${\kappa_{e}(\gamma)} = {\kappa_{\min} + {\left( {\kappa_{\max} - \kappa_{\min}} \right)\frac{q\left( {1 - \gamma} \right)}{q + \gamma}}}$

Methods of designing a microchannel layout for the inlet region 32 of aflow field begin with defining a fluid flow optimization domain withboundary conditions and loads. A gradient-based algorithm may then beused, together with computational fluid dynamics (CFD), to optimize thedomain for minimum flow resistance. FIG. 5 illustrates the use of finiteelement analysis to update design variables using an exemplary method ofmoving asymptotes (MMA) or a globally convergent method of movingasymptotes (GCMMA) algorithm that is looped in with the fluid flow CFD.In various aspects, the methods for minimizing the flow resistanceinclude minimizing the fluid power and/or pressure drop. For the fluidinlet boundary conditions, a first option includes a specified velocityand a second option includes a zero pressure; other conditions such as aspecified mass flow rate are possible, as well. For the fluid outletboundary conditions, the first option includes a zero pressure, and thesecond option includes a specified velocity. Subject to a solid materialvolume constraint, for example 50%, the objective function F to minimizeis based on the following relationship:

$F_{o} = {\int\limits_{\Omega}{\left\lbrack {{\frac{1}{2}\eta {\sum\limits_{i,j}\left( {\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}} \right)^{2}}} + {\sum\limits_{i}{{\kappa_{e}(\gamma)}u_{i}^{2}}}} \right\rbrack d\; \Omega}}$

The function generally represents the quantity that is being minimizedfor best performance, here that is the minimization of flow resistanceacross the structure for better efficiency. Minimization of flowresistance is important because it is directly related to pumping power.In various aspects, the design space Ω may be defined to provide regionsthat cannot be modified during the course of the optimization.Evaluation of the objective function can be performed solvingdifferential equations using a finite element method or similarcomputational approach.

In other aspects, the methods may include using the gradient-basedalgorithm together with computational fluid dynamics to optimize theporous media model domain for a uniform flow velocity or a minimum flowvelocity in a certain direction, for example, along an axis. Withrenewed reference to FIG. 1, the fluid flow optimization domain mayinclude an x-axis defining a longitudinal direction from an inlet 24leading to an outlet 26 of the flow field, a y-axis defining atransverse direction with respect to the x-axis, and a z-axisperpendicular to the both x-axis and the y-axis. In certain aspects, aflow velocity can be optimized for uniformity by taking into account adifference in the flow velocity in a direction of the x-axis isminimized according to a relationship of:

$\left\lbrack \frac{u - u_{{out}_{avg}}}{u_{{out}_{avg}}} \right\rbrack^{2}$

wherein u represents a local velocity in the direction of the x-axisexiting a channel of the outlet window, and u_(out avg) represents anoptimized target velocity in the direction of the x-axis exiting achannel of the outlet window. In certain other aspects, the methods mayinclude using the gradient-based algorithm together with computationalfluid dynamics to optimize the porous media model domain for a minimumflow velocity in a direction of the y-axis. In this regard, the methodsmay include determining a difference in flow velocity in a direction ofthe y-axis that is minimized according to a relationship of: v², whereinv represents a local velocity in the direction of the y-axis.

FIGS. 7 and 8 illustrate the comparison between traditional topologyoptimization and porous media design. FIG. 7 provides the situation withthe inverse permeability κ_(min) being equal to zero, and represents astrictly black & white (0, solid and 1, fluid) design, illustrating purefluid flow from the inlet 24 shown with fluid streamlines, generallyrepresented by reference number 36 that, as shown, exits via roughly 146outlets (each outlet is not separately shown). One issue that ariseswith the configuration of FIG. 7, however, is that when there is a largeopen volume for a flow channel (pure fluid), there is no structureavailable to support other components of the fuel cell, such as themembrane. Methods of the present technology include setting the minimuminverse permeability to a non-zero value and obtaining a grayscaledesign and fluid velocity field. FIG. 8 provides an exemplary grayscaledesign representing a porous medium with the inverse permeabilityκ_(min) being equal to one third of the maximum, for example,κ_(min)=0.333 κ_(max), so there is not any area that is a pure fluid,instead it is all porous. The grayscale of FIG. 8 is now representativeof the porous medium fluid flow from the inlet 24 via the tailoredpermeability fluid streamlines, generally represented by referencenumber 38, that essentially exits via one outlet.

In various aspects, an effective medium theory approach may be used inorder to obtain a width/channel spacing of the microchannels. Forexample, a functionally graded porous flow medium can be translated intoa microchannel network, where the permeability of the porous mediumcontains embedded information about microchannel dimensions.

Traditional topology optimization does not retain microchannels.However, the present technology utilizes information embedded in theinverse permeability field to guide the relative design of themicrochannel structure in order to obtain fine scale features. Forexample, the inverse permeability can provide a relationship betweenporous media and microchannel design utilizing an effective mediumapproach where, for example, the microchannel spacing scales with thesquare of the channel width. It should be noted that other scalefunctions may be contemplated. In this regard, the full Navier-Stokesapproach is employed for narrow channels for the fluid flow assessments.Each microchannel can be modeled as a fluid-saturated porous medium,numerically solved using the modified Forchheimer-Brinkman-extendedDarcy equation for the fluid flow:

${{{{- \frac{d}{dx}}{\langle p\rangle}_{f}} + {\mu_{f}\frac{d^{2}}{{dy}^{2}}{\langle u\rangle}_{f}} - \frac{\mu_{f}}{K}} \in {\langle u\rangle}_{j}} = 0$

which leads to the following relationships:

${\epsilon = \frac{w_{c}}{w}},{K = \frac{\epsilon \; w_{c}^{2}}{12}},{k_{sc} = {\left( {1 - \epsilon} \right)k_{i}}},{k_{fe} = {\epsilon \; k_{f}}}$

See, e.g., S. J. Kim, D. Kim, Forced convection in microstructures forelectronic equipment cooling, ASME J. Heat Transfer 121 (1999) 635-645.The approach can be utilized to provide a relationship of permeability Kas a function of the microchannel width w_(c) and porosity ε, wherek_(se), k_(s), k_(fe), and k_(f) are the effective thermal conductivityof solid, thermal conductivity of the solid, effective thermalconductivity of fluid, and thermal conductivity of fluid, respectively.In this regard, the microchannel pitch/spacing is logically linked tothe permeability of the design porous material layout; for example, itdirectly relates the microstructure of the porous material to thedimensions of a channel structure.

Once the grayscale design and fluid velocity fields are obtained, invarious aspects, exemplary methods include using the Gray-Scott reactiondiffusion equations in order to model and obtain a microchannel layout,for example, to obtain generate a variable pitch microchannel pattern.Once a microchannel layout is obtained, it can be used as a pattern fora flow field area of a bipolar plate.

As is known in the art, reaction-diffusion systems are mathematicalmodels that correspond to physical phenomena. In one example, a changein space and time of the concentration of one or more chemicalsubstances is modeled. In mathematical terms, reaction-diffusion systemsgenerally take the form of semi-linear parabolic partial differentialequations represented by the general form as follows:

∂_(t) q=D∇ ² q+R(q),

where q(x, t) represents the unknown vector function, D is a diagonalmatrix of diffusion coefficients, and R accounts for all localreactions. Reaction and diffusion of chemical species can produce avariety of patterns, reminiscent of those often seen in nature. TheGray-Scott equations model such a reaction and are generally provided asfollows:

${\frac{\partial u}{\partial t} = {{D_{u}{\nabla^{2}u}} - {uv}^{2} + {F\left( {1 - u} \right)}}},{\frac{\partial v}{\partial t} = {{D_{v}{\nabla^{2}v}} + {uv}^{2} - {\left( {F - k} \right){v.}}}}$

The partial differential equations modeling this process may besimulated with a variety of numerical techniques. In various aspects,good results can be obtained using methods such as forward Eulerintegration of the finite-difference equations that one obtains byspatial discretization of the Laplacian, or the diffusion coefficientscan be estimated for a target pitch/spacing. For example, in variousaspects the value of (pitch){circumflex over ( )}2 (i.e. the square ofthe microchannel width) can be used to approximate the diffusioncoefficient.

The Gray-Scott reaction diffusion model is a mathematical model thatdescribes the behavior of two chemical substances and calculates theconcentration of the two substances at a given time based upon thesubstances diffusion, feed rate, removal rate, and a reaction betweenthe two. This simulation not only models the underlying process of achemical reaction but can also result in patterns of the substances thatare remarkably similar to patterns found in nature. Examples includepatterns on animals, such as stripes on zebras, a leopard's skin, spotson butterflies, patterns on fish; fingerprints; ripples on sand;patterns of veins on a leaf; and various other biological phenomena.With the present technology, certain of the patterns resulting from thismodel can be used for the design of at least a portion of a flow fieldof a bipolar plate.

To illustrate the model, one analogy presented is to imagine an area orspace containing various concentrations of each chemical substance U andV at time zero. Over time, substance U is fed into the reaction at agiven rate, while substance V is removed at a given rate. Further, twomolecules of V can react with one of U, which converts the substance ofU to V as follows:

U+2V→3V

V→P

U, V, and P are chemical substances. A simulation is accomplished usingthe two partial differential equations listed above, each representingthe change in concentration of a substance over time, where u and v areindependent variables that represent their respective concentrations;D_(u) and D_(v) are their respective diffusion rates or diffusiontensors, which can be calculated from permeability. The parameter krepresents the rate of conversion of V to P; and F represents the rateof process that feeds U and drains U, V, and P. The parameters k and Fare arbitrary positive numbers that can be adjusted. Each diffusiontensor is generally a 3×3 matrix reflecting diffusion rates in differentdirections.

The change in u (upper partial differential equation) is dependent uponits reaction with v (hence the subtraction (−) of uv²) and is fed at acertain rate (+F, scaled to its current concentration). The change in v(lower partial differential equation) is dependent upon its reactionwith u (hence the addition (+) of uv²), and is removed at a given rate(−k, scaled by the feed rate and concentration of V). The concentrationof U or V at each position is updated at each time increment(typically 1) based upon the result of the corresponding equation. Thevalues for the feed rate, removal rate, and diffusion rate are enteredinto the equations. For example, on a 2D grid, the Laplacian Operatorcould be calculated on a convolution matrix. To calculate the newconcentration, the current concentration and each surroundingconcentration is multiplied by the corresponding value in the matrix(where the current position corresponds to the center position in theconvolution matrix) and all values summed. This value technicallyrepresents the difference in concentrations between the current positionand the surrounding positions.

The above model can be programmed in a suitable computer code as isknown in the art. In various aspects, the resulting model provides animage representing the reaction container, with each point or pixel ofthe image representing the concentration of V (v) at that position. Forexample, the Gray-Scott reaction diffusion equations can be solved withvarious numerical methods, such as the finite differential method or thefinite element method. The initial value of u and v could be randomnoise distribution. By solving the Gray-Scott equations for some timeperiod with an appropriate parameter set, a steady state is obtained.Then, the obtained distribution is interpreted as a channel structure.For instance, u>th may represent the wall domain and u<th may representthe channel domain, where th is a threshold value.

Notably, the diffusion tensor is coupled with the permeabilitydistribution of the flow system to be designed. For example, thepermeability distribution is projected to the channel pattern with avariable array pitch through the diffusion coefficient distribution ofthe Gray-Scott equations. The circles A and B in FIG. 8 illustrate, byway of non-limiting examples, certain areas of the flow field that maybe provided with a fine pitch, represented by circle A, and with acoarse pitch, represented by circle B.

In various aspects, the present technology may use the Gray-Scottreaction diffusion equations with the grayscale design and fluidvelocity field to obtain an anisotropic microchannel layout. This mayinclude using an anisotropic diffusion tensor with the Gray-Scottequations. FIG. 9 illustrates an exemplary method flow chart fordesigning a pattern for an inlet region of a flow field using ananisotropic diffusion tensor.

In various aspects, a weak and strong anisotropic tensor set isalternatively used to obtain the connected line and space pattern, alongwith the flow direction. With an isotropic diffusion tensor, the ratioof the microchannel pitch (a) to the length (b) can be represented asa:b=1:1. For a weakly anisotropic tensor, the ratio of a:b is betweenabout 1:1 to about 1:5. For a strongly anisotropic tensor, the ratio ofa:b may be up to about 1:100. As noted in FIG. 9, the lateral directiondefines the channel pitch. By stretching the tensor in the longitudinaldirection, which is the flow direction, the line and space pattern canbe obtained. In various aspects, at least two sets of diffusion tensorsare used to repeatedly solve the reaction diffusion equations: anisotropic or weakly anisotropic set, and a strongly isotropic set. Invarious methods, the Gray-Scott equations may be solved for some timeperiod, where the diffusion tensor sets alternate in strength from weakto strong. For example, the diffusion tensor may be switched fromisotropic→anisotropic→isotropic. This may be repeated several times,preferably finishing with either a weakly anisotropic set or completelyisotropic set. FIG. 10 illustrates an exemplary schematic generallysummarizing methods for designing a pattern for an inlet region of aflow field.

Pending patent application Ser. No. 16/275,394, filed on Feb. 14, 2019,which has the same inventors and common ownership with the presentapplication, provides various illustrations showing the differences indesign of the flow field based on the type of diffusion tensor(s) used,and is incorporated by reference herein in its entirety. As providedtherein, an initial random pattern can be obtained from the Gray-Scottequations using a single diffusion tensor to obtain an inlet flow fieldusing a single isotropic diffusion tensor set, with a ratio of a:b as1:1. In contrast, an inlet flow field using a single weakly anisotropicdiffusion tensor set can be obtained from the Gray-Scott equations, witha ratio of a:b as 1:5, and an inlet flow field using a single stronglyanisotropic diffusion tensor set obtained from the Gray-Scott equations,with a ratio of a:b as 1:100. Inlet regions of flow fields may beprovided with a combination of diffusion tensors resulting in anoptimized microchannel design, including: alternating from stronglyanisotropic to isotropic; alternating from isotropic, to stronglyanisotropic, to isotropic; alternating from strongly anisotropic, toisotropic, to strongly anisotropic, back to isotropic.

Once the pattern of the flow field is generally designed with amicrochannel layout, various channels of the flow field, at least in theinlet region 32, are then defined having discrete areas of discontinuity(reference number 58 of FIGS. 15, 16, and 18) that ultimately provide anincreased uniformity in fluid flow. In various aspects, the discreteareas of discontinuity 58 are aligned and located along or near spacedapart contour lines 54 that may be based on a predetermined performanceparameter of the bipolar plate. For example, the predeterminedperformance parameter may be at least one of pressure flow, discussedbelow with respect to FIGS. 11-16, and velocity flow, discussed belowwith respect to FIGS. 17-19.

FIG. 11 illustrates an exemplary pressure field 50 obtained from anoptimized porous media flow field model for flow from an inlet 24 andthrough the inlet region 32, exiting an outlet window region 52ultimately leading through to the other side of the flow field 28 (FIG.1). As shown, a plurality of spaced apart contour lines 54 are providedsubstantially aligned with predetermined boundaries of changes inpressure. The contour lines 54 indicate pressure boundaries asillustrated in a color range from dark red (highest pressure) to darkblue (lowest pressure), with the color scale providing contour pressure(in units of Pa) and the numerical scale providing contour pressure (inunits of Pa). FIG. 12 illustrates a line graph of a velocity profileassociated with the pressure field of the optimized porous media inletflow field model of FIG. 11 that corresponds to one theoretical outletflow channel. For purposes of providing an example flow field, FIGS.13-19 are intended to have 113 representative flow channels at theoutlet window region 52 and extending in a direction along the x-axis(FIG. 1).

FIG. 13 illustrates a resulting pressure field 50 obtained from acontinuous channel design of the optimized porous media inlet flow fieldmodel of FIG. 11. As noted in the area designated with reference number56, a rate of branching of the channels 40 is not consistent, leading topressure and flow non-uniformity. As shown, a plurality of spaced apartcontour lines 54 are provided substantially aligned with predeterminedboundaries of changes in pressure. The contour lines 54 indicatepressure boundaries as illustrated in a color range from dark red(highest pressure) to dark blue (lowest pressure), with the color scaleproviding contour pressure (in units of Pa) and the numerical scaleproviding contour pressure (in units of Pa). The pressure field 50 ofFIG. 13 indicates a non-uniformity in pressure at the outlet windowregion 52. FIG. 14 illustrates a line graph of a velocity profileassociated with the pressure field of the continuous channel inlet flowfield design of FIG. 13, clearly indicating the flow non-uniformitybetween the flow channels.

FIG. 15 illustrates a resulting pressure field 50 obtained from adiscontinuous channel design of the optimized porous media inlet flowfield model of FIG. 11. The pressure field 50 is provided having asubstantially uniform inlet feed rate in the region 60 immediatelyadjacent the inlet 24. The pattern includes a plurality of channels 40defined by a plurality of side walls 42 with discrete areas ofdiscontinuity 58. The contour lines 54 indicate pressure boundaries asillustrated in a color range from dark red (highest pressure) to darkblue (lowest pressure), with the color scale providing contour pressure(in units of Pa) and the numerical scale providing contour pressure (inunits of Pa). The pressure field 50 of FIG. 15 having the discrete areasof discontinuity 58 indicates a uniformity in pressure at the outletwindow region 52. As shown, the discontinuous channel design of thepresent technology is able to nearly exactly recover the porous modelpressure field distribution provided in FIG. 11. In various aspects,locating the discrete areas of discontinuity 58 with the plurality ofcontour lines 54 of the pressure field provides a variation of fluidflow pressure between channels of the outlet window region 52 of theinlet region 32 of the flow field and the porous media model domain ofless than about 7%, less than about 5%, and even less than about 3%.

FIG. 16 illustrates an exemplary design of a flow field 62 with adiscontinuous channel inlet flow field design according to anotheraspect of the present technology.

Differentiated from FIG. 15, the design of FIG. 16 provides a patternhaving a non-uniform inlet feed rate in the region 64 immediatelyadjacent the inlet 24. The pattern includes a plurality of channels 40defined by a plurality of side walls 42 with discrete areas ofdiscontinuity 58. As shown, many of the discrete areas of discontinuity58 are aligned and located with contour lines 58 representative of apredetermined performance factor of the bipolar plate. The pressurefield 62 of FIG. 16 having the discrete areas of discontinuity 58similarly indicates a uniformity in pressure at the outlet window region52.

FIG. 17 illustrates an exemplary velocity field 66 obtained from anoptimized porous media inlet flow field model for flow from an inlet 24and through the inlet region 32, exiting an outlet window region 52ultimately leading through to the other side of the flow field 28. Asshown, a plurality of spaced apart arrows 68 are provided to representdirection and relative magnitude of the velocity. The contoured colorregions indicate a central area 70 with a higher velocity and indicatevelocity boundaries as illustrated in a color range from dark red(highest velocity) to dark blue (lowest velocity), with the color scaleproviding contour velocity (in units of m/s).

FIG. 18 illustrates a resulting velocity field 66 obtained from adiscontinuous channel design model of the optimized porous media inletflow field model of FIG. 17. The pattern includes a plurality ofchannels 40 defined by a plurality of side walls 42 with discrete areasof discontinuity 58. The contoured color regions indicate velocityboundaries as illustrated in a color range from dark red (highestvelocity) to dark blue (lowest velocity), with the color scale providingflow velocity (in units of m/s). The velocity field 66 of FIG. 18 havingthe discrete areas of discontinuity 58 indicates a uniformity in flowvelocity at the outlet window region 52. As shown, the discontinuouschannel design of the present technology is able to nearly exactlyrecover the porous model velocity field distribution provided in FIG.17. In various aspects, locating the discrete areas of discontinuity 58with the plurality of contour lines of the velocity field provides avariation of fluid flow velocity between channels of the outlet windowregion 52 of the inlet region 32 of the flow field and the porous mediamodel domain of less than about 7%, less than about 5%, and even lessthan about 3%.

FIG. 19 is a graph that shows the results of a comparison between adiscontinuous channel inlet velocity field and a target specificationvelocity field. The average outlet velocity is 0.124 m/s. The averageflow non-uniformity is about 4.5%, relative to the average outletvelocity. The maximum flow non-uniformity is about 9.7%, relative to theaverage outlet velocity.

Once an optimized microchannel layout and design is obtained andincorporated into a pattern, the present technology also provides forthe manufacturing of the channels and creating the flow field of thebipolar plate, optionally with a tailored porosity. FIG. 20 provides across-section view of an exemplary set of basic channels 40, walls 42,and bottom portion 44 of an inlet flow field 32 that can be madeaccording to various manufacturing techniques. It should be understoodthat the specific design of the channels and walls can be quite detailedin various aspects.

Numerous materials and fabrication techniques can be used, incombination with the pattern, to create a network of a plurality ofchannels/microchannels 40 defined by a plurality of side walls 42 invarious regions of a flow field. In various aspects, the presenttechnology is particularly useful with functionally graded materialsand/or microchannels, a porous media, or a hybrid combination thereof. Afunctionally graded material (“FGM”), also referred to as a functionallygraded porous material, is generally known in the art as a material witha changing composition, microstructure, and/or porosity across a volumeof the material, in one or more direction. FGMs can be specificallydesigned to perform a set of specified functions, and have almostendless possibilities for tailoring and customization, which can be veryuseful in making a flow field, or portion thereof, for a bipolar plate.Design parameters of the FGM can be used with the effective mediumtheory, as described above, in order to translate a FGM into amicrochannel network, where at least one dimension of the microchannels,such as a width, is based on a permeability of the FGM. FGMs cangenerally be classified as being porosity and pore sizegradient-structured, chemical/composition gradient-structured, andmicrostructural-gradient structured; each of which can be used singly orin combination with the flow field patterns designed herein. Not onlydoes the present technology envision shaping and/or machining anexisting FGM into a pattern, but also contemplates the creation of FGMsusing additive manufacturing and similar techniques and technologies.For example, microstructural gradient functionally gradient material canbe additive manufactured such that the microstructure is tailored sothat different microstructures are produced in the material, which ismade to change gradually, so as to achieve the desired properties fromthe material. In certain aspects, microstructural gradation can also beachieved during a solidification process using quenching. In otheraspects, sintering techniques can be useful to produce a varyingmicrostructure within a material.

In the broadest sense, additive manufacturing techniques can be used tomake a pattern in the flow field, or portion thereof, where it isdesired that at least a portion of the flow field is custom made andtailored to a specific design. Various non-limiting examples of additivemanufacturing techniques include fabricating using laser sinteringtechniques, selective laser melting and electron-beam meltingtechniques, 3-D printing, and/or using binder jet technology that mayuse a combination of printing and curing. In other aspects, variouselectroplating techniques may also be used for fabricating or workingwith a functionally graded porous medium. Certain composite materials,polymers, thermoplastics, resins, and the like may be considered asuseful materials, depending on the patterns and designs.

In still other aspects, metal inverse opal (“MIO”) technology can beused with a suitable metal, such as copper, nickel, titanium, and thelike. MIO technology can be tailored and customized as is known in theart. In one common example, a functionally graded porous medium cangenerally be obtained by templating polystyrene particles of differentsizes, and/or controlling a sintering time for different templatedregions. If desirable, MIO techniques can be used that create necks,pores, and fluidic routing structures exerting specific capillaryforces, wicking, and flow patterns. Conventional metal machining and/orstamping techniques can be used in combination with the above techniquesto ultimately provide the bipolar plates having flow fields withvariable pitch microchannel designs.

Various hybrid porous structured materials and combinations of materialsand methods of manufacture can also be used with the present technology.Hybrid porous structured materials may include a porous region and anon-porous region. Metal foams, and the like, may also be incorporatedwith designs of the present technology as a functionally graded porousmaterial. In various aspects, dense, non-porous channel walls 42 can beprovided with a coating of a porous material. Certain designs mayinclude dense walls 42 with a porous bottom wall 44. In other aspects,the channel walls 42 may be made of a porous material or FGM, and thebottom wall 44 can be non-porous. The changes in porosity can also begradient. In still other aspects, one or more regions of the bottom wall44 can be designed to have a first degree of porosity, while the channelwalls 42 may have a second degree of porosity, and so on. In certainaspects, the bottom wall 44 may be a part of the substrate or bipolarplate, and a plurality of microchannels may be subsequently created froma FGM, or formed on the bipolar plate using additive manufacturing,electroplating, or a combination thereof in order to create a variablepitch microchannel pattern configured to direct fluid from an inlet toan outlet.

The foregoing description is provided for purposes of illustration anddescription and is in no way intended to limit the disclosure, itsapplication, or uses. It is not intended to be exhaustive or to limitthe disclosure. Individual elements or features of a particularembodiment are generally not limited to that particular embodiment, but,where applicable, are interchangeable and can be used in a selectedembodiment, even if not specifically shown or described. The same mayalso be varied in many ways. Such variations should not be regarded as adeparture from the disclosure, and all such modifications are intendedto be included within the scope of the disclosure.

As used herein, the phrase at least one of A, B, and C should beconstrued to mean a logical (A or B or C), using a non-exclusive logical“or.” It should be understood that the various steps within a method maybe executed in different order without altering the principles of thepresent disclosure. Disclosure of ranges includes disclosure of allranges and subdivided ranges within the entire range, including theendpoints.

The headings (such as “Background” and “Summary”) and sub-headings usedherein are intended only for general organization of topics within thepresent disclosure, and are not intended to limit the disclosure of thetechnology or any aspect thereof. The recitation of multiple embodimentshaving stated features is not intended to exclude other embodimentshaving additional features, or other embodiments incorporating differentcombinations of the stated features.

As used herein, the terms “comprise” and “include” and their variantsare intended to be non-limiting, such that recitation of items insuccession or a list is not to the exclusion of other like items thatmay also be useful in the devices and methods of this technology.Similarly, the terms “can” and “may” and their variants are intended tobe non-limiting, such that recitation that an embodiment can or maycomprise certain elements or features does not exclude other embodimentsof the present technology that do not contain those elements orfeatures.

The broad teachings of the present disclosure can be implemented in avariety of forms. Therefore, while this disclosure includes particularexamples, the true scope of the disclosure should not be so limitedsince other modifications will become apparent to the skilledpractitioner upon a study of the specification and the following claims.Reference herein to one aspect, or various aspects means that aparticular feature, structure, or characteristic described in connectionwith an embodiment or particular system is included in at least oneembodiment or aspect. The appearances of the phrase “in one aspect” (orvariations thereof) are not necessarily referring to the same aspect orembodiment. It should be also understood that the various method stepsdiscussed herein do not have to be carried out in the same order asdepicted, and not each method step is required in each aspect orembodiment.

What is claimed is:
 1. A method for designing a microchannel layout fora flow field of a bipolar plate, the method comprising: defining a fluidflow optimization domain with boundary conditions and loads, the fluidflow optimization domain including an x-axis defining a longitudinaldirection from an inlet leading to an outlet of the flow field, a y-axisdefining a transverse direction with respect to the x-axis, and a z-axisperpendicular to both the x-axis and the y-axis; using a gradient-basedalgorithm together with computational fluid dynamics to optimize aporous media model domain; setting a minimum inverse permeability to anon-zero value, and obtaining a grayscale design and fluid velocityfield; using Gray-Scott reaction diffusion equations with the grayscaledesign and fluid velocity field to obtain a microchannel layout with aplurality of channels; providing the plurality of channels with discreteareas of discontinuity; incorporating the microchannel layout as apattern for an inlet region of the flow field of the bipolar plate. 2.The method according to claim 1, further comprising developing aplurality of contour lines in the flow field, wherein the plurality ofcontour lines are spaced apart based on a predetermined performanceparameter of the bipolar plate.
 3. The method according to claim 2,further comprising locating the discrete areas of discontinuity with theplurality of contour lines.
 4. The method according to claim 3, furthercomprising determining an optimized pressure field for the flow field,wherein the optimized pressure field is used as the predeterminedperformance parameter to define the plurality of contour lines based ondifferences in pressure.
 5. The method according to claim 4, whereinlocating the discrete areas of discontinuity with the plurality ofcontour lines of the pressure field provides a variation of fluid flowpressure between channels of the outlet window of the flow field and theporous media model domain of less than about 5%.
 6. The method accordingto claim 3, further comprising determining an optimized velocity fieldfor the flow field, wherein the optimized velocity field is used as thepredetermined performance parameter to define the plurality of contourlines based on differences in velocity.
 7. The method according to claim6, wherein locating the discrete areas of discontinuity with the contourlines of the velocity field provides a variation of fluid flow velocitybetween channels of the outlet window of the flow field and the porousmedia model domain of less than about 5%.
 8. The method according toclaim 1, comprising using the gradient-based algorithm together withcomputational fluid dynamics to optimize the porous media model domainfor minimum flow resistance across the porous media model domain.
 9. Themethod according to claim 8, wherein using the gradient-based algorithmtogether with computational fluid dynamics to optimize the porous mediamodel domain for minimum flow resistance comprises using a modifiedDarcy flow equation for porous media.
 10. The method according to claim1, comprising using the gradient-based algorithm together withcomputational fluid dynamics to optimize the porous media model domainfor a uniform flow velocity in a direction of the x-axis.
 11. The methodaccording to claim 1, comprising using the gradient-based algorithmtogether with computational fluid dynamics to optimize the porous mediamodel domain for a minimum flow velocity in a direction of the y-axis.12. The method according to claim 1, comprising using Gray-Scottreaction diffusion equations with the grayscale design and fluidvelocity field to obtain an anisotropic microchannel layout with aplurality of channels.
 13. The method according to claim 12, comprisingusing a weak and strong anisotropic diffusion tensor set alternativelyto obtain a connected line and space pattern for the anisotropicmicrochannel layout.
 14. A method for designing an anisotropicmicrochannel layout for a flow field of a bipolar plate, the methodcomprising: defining a fluid flow optimization domain with boundaryconditions and loads; using a gradient-based algorithm together withcomputational fluid dynamics to optimize a porous media model domain;setting a minimum inverse permeability to a non-zero value, andobtaining a grayscale design and fluid velocity field; using Gray-Scottreaction diffusion equations and an anisotropic diffusion tensor alongwith the grayscale design and fluid velocity field and to generate ananisotropic microchannel layout having a connected line and spacepattern including a plurality of channels; providing the plurality ofchannels with discrete areas of discontinuity; and incorporating theanisotropic microchannel layout as a pattern for an inlet region of theflow field of the bipolar plate to provide flow uniformity.
 15. Themethod according to claim 14, comprising using the gradient-basedalgorithm together with computational fluid dynamics to optimize theporous media model domain for a minimum flow resistance across thedomain.
 16. The method according to claim 14, comprising using thegradient-based algorithm together with computational fluid dynamics tooptimize the porous media model domain for a uniform velocity across adirection of the domain.
 17. The method according to claim 14,comprising using the gradient-based algorithm together withcomputational fluid dynamics to optimize the porous media model domainfor a minimum velocity across a direction of the domain.
 18. The methodaccording to claim 14, comprising using a weak and strong anisotropicdiffusion tensor set alternatively to solve the Gray-Scott reactiondiffusion equations, and determining a spacing of microchannels based oneffective medium theory, wherein the discrete areas of discontinuity aredisposed along spaced apart contour lines based on a predeterminedperformance parameter of the bipolar plate selected from at least one ofpressure flow and velocity flow.
 19. A bipolar plate for a fuel cell,the bipolar plate comprising: an inlet; an outlet; and a flow fieldhaving an inlet region comprising a pattern defining a plurality ofanisotropic microchannels configured to provide fluid communicationbetween the inlet and the outlet, the anisotropic microchannels definedhaving discrete areas of discontinuity; wherein the pattern is designedusing an inverse permeability field and solving Gray-Scottreaction-diffusion equations with an anisotropic diffusion tensor toobtain an anisotropic microchannel layout with channel spacing based oneffective medium theory.
 20. The bipolar plate according to claim 19,wherein the discrete areas of discontinuity are disposed along spacedapart contour lines based on a predetermined performance parameter ofthe bipolar plate selected from at least one of pressure flow andvelocity flow.